PFP Laboratory 4 - Revision history

Beh01 at 13:13, 7 October 2025

2025-10-07T13:13:29Z

Beh01 at 10:58, 29 September 2022

2022-09-29T10:58:31Z

Beh01 at 10:57, 29 September 2022

2022-09-29T10:57:16Z

Beh01: Created page with "== List of lists ==
link=https://youtu.be/voiTk64SaQM
Consider following type representing picture:
2022-09-29T10:25:49Z

Created page with "== List of lists == <div style="float: right"> 80px|link=https://youtu.be/voiTk64SaQM</div> Consider following type representing picture: <syntaxhigh..."

New page
== List of lists ==
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/voiTk64SaQM]]</div>
Consider following type representing picture:
<syntaxhighlight lang="Haskell">type Pic = [String]</syntaxhighlight>
If you want to print this picture you can use:
<syntaxhighlight lang="Haskell">
pp :: Pic -> IO ()
pp x = putStr (concat (map (++"\n") x))
</syntaxhighlight>
Picture example:
<syntaxhighlight lang="Haskell">
pic :: Pic
pic = [ "....#....",
"...###...",
"..#.#.#..",
".#..#..#.",
"....#....",
"....#....",
"....#####"]
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> pp pic
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
</syntaxhighlight>
Create functions that:
Flips picture veriticaly and horizontally.
<syntaxhighlight lang="Haskell">
flipV :: Pic -> Pic
flipH :: Pic -> Pic</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> pp(flipV pic)
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
#####....
Main> pp(flipH pic)
....#####
....#....
....#....
.#..#..#.
..#.#.#..
...###...
....#....
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
flipV :: Pic -> Pic
flipV = map reverse

flipV' :: Pic -> Pic
flipV' xs = [reverse x|x<-xs]

flipH :: Pic -> Pic
flipH = reverse
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/DQJNA44418]]
</div>
<div style="clear:both"></div>

Place one picture above another.
<syntaxhighlight lang="Haskell">above :: Pic -> Pic -> Pic</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> pp(above pic pic)
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
above :: Pic -> Pic -> Pic
above x y = x ++ y
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/VTCE65032]]
</div>
<div style="clear:both"></div>

Place two pictures side by side (consider, that they have the same height).
<syntaxhighlight lang="Haskell">sideBySide :: Pic -> Pic -> Pic</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> pp(sideBySide pic pic)
....#........#....
...###......###...
..#.#.#....#.#.#..
.#..#..#..#..#..#.
....#........#....
....#........#....
....#####....#####
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
sideBySide :: Pic -> Pic -> Pic
sideBySide xs ys = map (\(x,y) -> x ++ y)(zip xs ys)

sideBySide':: Pic -> Pic -> Pic
sideBySide' (x:xs) (y:ys) = (x ++ y) : sideBySide' xs ys
sideBySide' _ _ = []

sideBySide'' :: Pic -> Pic -> Pic
sideBySide'' = zipWith (++)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/VTCE65032]]
</div>
<div style="clear:both"></div>

Rotate picture to the left and to the right.
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/l9qIHTFsEV0]]
</div>
<syntaxhighlight lang="Haskell">
rotateR :: Pic -> Pic
rotateL :: Pic -> Pic
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> pp(rotateR pic)
.......
...#...
....#..
.....#.
#######
#....#.
#...#..
#..#...
#......
Main> pp(rotateL pic)
......#
...#..#
..#...#
.#....#
#######
.#.....
..#....
...#...
.......
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
toRow :: String -> Pic
toRow xs = map (\x -> [x]) xs -- [[x]|x<-xs]

rotateR :: Pic -> Pic
rotateR [x] = toRow x
rotateR (x:xs) = (rotateR xs) `sideBySide` (toRow x)

rotateR' :: Pic -> Pic
rotateR' x = foldl1 sideBySide (reverse (map toRow x))

rotateL :: Pic -> Pic
rotateL [x] = reverse(toRow x)
rotateL (x:xs) = reverse(toRow x) `sideBySide` (rotateL xs)

rotateL' :: Pic -> Pic
rotateL' x = foldl1 sideBySide (map (reverse.toRow) x)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/JXX12735]]
</div>
<div style="clear:both"></div>

== User defined data types and type classes ==
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/lo0pdwWoSx4]]</div>
Consider following representation of expressions
<syntaxhighlight lang="Haskell">
data Expr = Num Int
| Add Expr Expr
| Sub Expr Expr
| Mul Expr Expr
| Div Expr Expr
| Var Char
deriving (Eq)
</syntaxhighlight>
Create function eval that evaluates expresions.
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/AvThE0I4Iz8]]</div>
<syntaxhighlight lang="Haskell">
eval :: Expr -> Int
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> eval (Add (Num 1) (Num 2))
3
Main> eval (Mul (Add (Num 1) (Num 2)) (Num 3))
9
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
eval :: Expr -> Int
eval (Num x) = x
eval (Add l r) = (eval l) + (eval r)
eval (Sub l r) = (eval l) - (eval r)
eval (Mul l r) = (eval l) * (eval r)
eval (Div l r) = (eval l) `div` (eval r)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

* Create function showExpr that shows expression as a String.
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/cPL1zEZHLh0]]</div>
<syntaxhighlight lang="Haskell">
showExpr :: Expr -> String
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> showExpr (Add (Num 1) (Num 2))
"1+2"
Main> showExpr (Mul (Add (Num 1) (Num 2)) (Num 3))
"(1+2)3"
Main> showExpr (Mul (Add (Num 1) (Mul (Num 2) (Var 'x'))) (Mul (Num 3) (Var 'x')))
"(1+2x)3x"
Main> showExpr (Mul (Num 2) (Mul (Var 'x') (Var 'x')))
"2xx"
</syntaxhighlight>
<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
showExpr :: Expr -> String
showExpr expr = showExpr' expr NoOp

data Operation = Hi | HiDiv | Lo | LoSub | NoOp deriving (Eq)

showExpr' :: Expr -> Operation -> String
showExpr' (Num x) _ = show x
showExpr' (Var x) _ = [x]
showExpr' (Add l r) op = let
x = showExpr' l Lo ++"+"++showExpr' r Lo
in if op == Hi || op == HiDiv || op==LoSub
then "(" ++ x ++")"
else x
showExpr' (Sub l r) op = let
x = showExpr' l Lo ++"-"++showExpr' r LoSub
in if op == Hi || op == HiDiv || op==LoSub
then "(" ++ x ++")"
else x
showExpr' (Mul l r) op = let
x = showExpr' l Hi ++""++showExpr' r Hi
in if op == HiDiv
then "(" ++ x ++")"
else x
showExpr' (Div l r) op = let
x = showExpr' l Hi ++"/"++showExpr' r HiDiv
in if op == HiDiv
then "(" ++ x ++")"
else x
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

Extend class Show to be usable with our expressions.
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/NCAxJx_wJxI]]</div>
<syntaxhighlight lang="Haskell" class="myDark">
Main> Add (Num 1) (Num 2)
"1+2"
Main> Mul (Add (Num 1) (Num 2)) (Num 3)
"(1+2)3"
Main> Mul (Add (Num 1) (Mul (Num 2) (Var 'x'))) (Mul (Num 3) (Var 'x'))
"(1+2x)3x"
Main> Mul (Num 2) (Mul (Var 'x') (Var 'x'))
"2xx"
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
instance (Show Expr) where
show = showExpr
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

* Create function derivation representing symbolic derivation of a given expression.
<syntaxhighlight lang="Haskell">
deriv :: Expr-> Char -> Expr
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
Main> deriv (Add (Num 1) (Num 2)) 'x'
0+0
Main> deriv (Mul (Num 2) (Mul (Var 'x') (Var 'x'))) 'x'
0xx+2(1x+x1)
Main> deriv (Mul (Num 2) (Mul (Var 'x') (Var 'x'))) 'x'
0xx+2(1x+x*1)
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
deriv :: Expr-> Char -> Expr
deriv (Num _) _ = (Num 0)
deriv (Var x) y | x==y = (Num 1)
| otherwise = (Num 0)
deriv (Add l r) x = Add (deriv l x) (deriv r x)
deriv (Sub l r) x = Sub (deriv l x) (deriv r x)
deriv (Mul l r) x = Add (Mul (deriv l x) r) (Mul l (deriv r x))
deriv (Div l r) x =
Div
(Sub (Mul (deriv l x) r) (Mul l (deriv r x)))
(Mul r r)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

← Older revision		Revision as of 10:57, 29 September 2022
Line 1:		Line 1:
		+	== List comprehension ==
		+	Using the list comprehension implement following functions:
		+
		+	* Create a function that generates a list of all odd numbers in given interval.
		+	<syntaxhighlight lang="Haskell">oddList :: Int -> Int -> [Int]</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> oddList 1 10
		+	[1,3,5,7,9]
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	oddList :: Int -> Int -> [Int]
		+	oddList a b = [ x \|x<-[a..b], odd x]
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/TXOOI93332]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	* Create a function that removes all upper case letters from a string.
		+	<syntaxhighlight lang="Haskell">removeAllUpper :: String -> String</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> removeAllUpper "ABCabcABC"
		+	"abc"
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	import Data.Char
		+
		+	removeAllUpper :: String -> String
		+	removeAllUpper xs = [ x \|x<-xs, not (isUpper x)]
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/TXOOI93332]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	* Create functions that computes union and intersection of two sets.
		+	<syntaxhighlight lang="Haskell">
		+	union :: Eq a => [a] -> [a] -> [a]
		+	intersection :: Eq a => [a] -> [a] -> [a]
		+	</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> union [1..5] [3..10]
		+	[1,2,3,4,5,6,7,8,9,10]
		+	*Main> intersection [1..5] [3..10]
		+	[3,4,5]
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	union :: Eq a => [a] -> [a] -> [a]
		+	union xs ys = xs ++ [y\| y<-ys, not (elem y xs)]
		+
		+	intersection :: Eq a => [a] -> [a] -> [a]
		+	intersection xs ys = [y\| y<-ys, elem y xs]
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/TXOOI93332]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	== More complex functions ==
		+	* Create a function that count the number of occurrences of all characters from a given string.
		+
		+	<div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/B2LFNJfC-TU]]</div>
		+	<syntaxhighlight lang="Haskell">countThem :: String -> [(Char, Int)]</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main>countThem "hello hello hello"
		+	[('h',3),('e',3),('l',6),('o',3),(' ',2)]
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	unique :: String -> String
		+	unique n = reverse(tmp n "") where
		+	tmp [] store = store
		+	tmp (x:xs) store \| x `elem` store = tmp xs store
		+	\| otherwise = tmp xs (x:store)
		+
		+	unique' :: String -> String
		+	unique' [] = []
		+	unique' (x:xs) = x: unique' (filter (/=x)xs)
		+
		+	countThem :: String -> [(Char, Int)]
		+	countThem xs = let u = unique xs
		+	in [(x, length (filter (==x) xs)) \|x<-u]
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/UVITE26792]]
		+	</div>
		+	<div style="clear:both"></div>
		+
		+	* Create a function that generates all combinations of given length from the characters from given string. You can assume, that all character are unique and the given length is not bigger then the length of this string.
		+	<div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/-muPoJucLyI]]</div>
		+	<syntaxhighlight lang="Haskell">combinations :: Int -> String -> [String]</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> combinations 3 "abcdef"
		+	["abc","abd","abe",...]
		+	</syntaxhighlight>
		+
		+	<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
		+	<syntaxhighlight lang="Haskell">
		+	combinations :: Int -> String -> [String]
		+	combinations 1 xs = [[x]\| x<-xs]
		+	combinations n (x:xs) \| n == length (x:xs) = [(x:xs)]
		+	\|otherwise = [[x] ++ y \|y<-combinations (n-1) xs ]
		+	++ (combinations n xs)
		+	</syntaxhighlight>
		+	[[File:Tryit.png\|center\|60px\|Try it!\|link=https://rextester.com/RTRV90066]]
		+	</div>
		+	<div style="clear:both"></div>
		+
	== List of lists ==		== List of lists ==
	<div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/voiTk64SaQM]]</div>		<div style="float: right"> [[File:Video logo.png\|80px\|link=https://youtu.be/voiTk64SaQM]]</div>

@@ Line 109: / Line 109: @@
 </div>
 <div style="clear:both"></div>
 == List of lists ==

@@ Line 288: / Line 288: @@
 </syntaxhighlight>
 [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/JXX12735]]
 </div>
 <div style="clear:both"></div>